Method for simulating a physical property of a technical structure by a component model

ABSTRACT

In a method for simulating a physical property of a component model in the form of a computer accessible construction model of a technical structure, a mesh of a component model is automatically generated. The component model is first described by a fine mesh of finite elements, and, based on the fine mesh, the natural oscillation behavior of the component model is determined. Based on the natural oscillation behavior, at least one area of the component model is determined, whose finite elements are less deformed than those of another area of the component model. The determined area of the component model is then described by a coarser mesh of finite elements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of PCT International Application No.PCT/EP2008/001605, filed Feb. 29, 2008, which claims priority under 35U.S.C. §119 to German Patent Application No. DE 10 2007 012 633.8, filedMar. 16, 2007, the entire disclosures of which are herein expresslyincorporated by reference.

This application contains subject matter related to U.S. applicationSer. No. 12/560,101, entitled “Automatic Mesh Generation Method forSimulating a Physical Property of a Technical Structure by a ComponentModel,” filed Sep. 15, 2009.

BACKGROUND AND SUMMARY OF THE INVENTION

The invention relates to a method and apparatus for simulating aphysical property of a technical structure, such as motor or a motorpart, by automatically generating a mesh of a component model, based onfinite elements, and to a corresponding computer program product.

The finite element method (FEM) is a widespread computation method inengineering. As depicted in FIG. 2, in the finite element method, acomputational domain 101 is divided into a large number of small, butmany, finite elements 102. On the basis of these elements trialfunctions are usually defined that produce a large system of equationsby way of a partial differential equation and the boundary conditions.Then the sought for results are derived from the solved system ofequations.

German patent document DE 10360150 A1 discloses a method for generatingthe envelope of a body based on a predetermined mesh of a constructionmodel in order to reproduce physical events on the surface of atechnical system through a finite element simulation.

German patent document DE 10326228 A1, on the other hand, discloses amethod for accelerating the meshing for finite element simulations of asystem with multiple bodies; and U.S. Pat. No. 6,044,210 discloses amethod for determining a finite element model for a structural element.

With standard software for finite element simulations, like ABAQUS, itis already possible to automatically mesh a component model (that is, todescribe it by means of a plurality of finite elements). In particular,it is already possible with this standard software to adapt FE (finiteelement) networks to an example of application. For example, ABAQUSprovides a so-called “adaptive remeshing,” which describes in a firststep a component model by means of a coarse FE network (synonymous with“coarse mesh of finite elements” or “coarse mesh with finite elements”).Then this network is automatically refined in an area where highmechanical stresses occur, in order to describe in a more suitablemanner the component model for additional calculations. The automaticrefinement is triggered as a function of the stress gradients betweentwo FE elements. In this procedure the stress gradient between the FEelements is determined, and if it exceeds a certain value, then thenetwork is refined at this point. As a result of the finer resolution,the stress gradient decreases.

This procedure is executed in an iterative manner until the stressgradients satisfy the established criteria. The finer the mesh, thebetter the mesh can usually describe the component model, the morememory space said model usually requires, and the more computationallyintensive the additional calculations or simulations, which are based onthis mesh, usually are.

One object of the present invention is to provide a method forsimulating a physical property of a technical structure (such asacoustic response) by automatically generating a mesh of a componentmodel, which requires little memory space and yet suitably describes(that is, closely accords with reality) the component model. In thiscontext, the component model may be, for example, a computer accessibleconstruction model of any technical system or any technical structure,like a motor or a motor element or a part of a motor element.

This and other objects and advantages are achieved by the method andapparatus according to the invention, which departs from the prior arttechnique of proceeding from a coarse mesh, in a step-by-step manner, toa finer mesh. Instead, the technique of the present invention isprecisely the reverse: to describe the component model 101 initially bymeans of a fine mesh (FIG. 2), and then taking this fine mesh as abasis, to pass, in particular, step by step, at least area by area, to acoarser mesh 103. (See FIG. 3.)

This strategy has the advantage that a decision about which area of acomponent model ought to be finely meshed and which area ought to becoarsely meshed is based on a fine mesh, so that it is more reliable orleads more directly to the target than in the prior art. This approachresults in a more adaptive mesh of a component model than in the priorart. Yet it can also make do with little memory space, especiallybecause of the specifically selected areas of the coarse mesh. Anadditional advantage lies in the fact that an automatic mesh is quitepossible, especially if the element size is small.

The present invention is based on the additional idea of pinpointingsuitable areas of the component model for description by means of acoarser mesh, by analyzing the deformation behavior of the finiteelements.

Other objects, advantages and novel features of the present inventionwill become apparent from the following detailed description of one ormore preferred embodiments when considered in conjunction with theaccompanying drawing.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a flow chart that illustrates the steps performed by thesimulation method according to the invention;

FIG. 2 shows schematically a fine mesh that characterizes a componentmodel; and

FIG. 3 shows the mesh of FIG. 2, which has been modified on anarea-by-area basis to include a coarser mesh.

DETAILED DESCRIPTION OF THE DRAWING

As shown in FIG. 1, for automatically generating a mesh of apredetermined component model (which is described, for example, by meansof CAD data), a preferred embodiment provides that the component model101 is described automatically, by means of a fine mesh of finiteelements 102 (or with finite elements) (Step S1). (See FIG. 2.)

Based on the fine mesh, a natural oscillation behavior of the componentmodel is determined automatically, especially in a predeterminedfrequency range of, for example, 100 hertz to 3,000 hertz (Step S2).Based on the natural oscillation behavior in Step S3, at least one areaof the component model is determined automatically, whose finiteelements are less deformed (or are deformed in a weaker manner) than thefinite elements of another area of the component model. (In particular,the finite elements are assigned by computation a weaker deformation.)The determined area is then described automatically by a coarser mesh offinite elements (Step S4), and is given more preference than beforeand/or than the other area of the component model (Step S5).

As a result, based on a fine mesh, the natural oscillation behavior ofthe component model and/or the deformation behavior of the finiteelements of the component model can be determined reliably andaccurately; and based on this accurate and reliable result, the areasthat are less deformed can be described selectively and accurately by acoarser mesh 103. The targeted coarser mesh of these areas has less of anegative influence on the quality of conformance, the adaptiveness, orthe quality of the whole mesh of the component model, than the coarsermesh of the areas in which the finite elements are highly deformed, orthan the arbitrary coarser mesh of the component model.

The mesh of the component model can therefore be mapped in a morememory-efficient manner, and can be further processed efficiently, whileat the same time it can still be described sufficiently adaptively thatsimulations which are based on the mesh of the component model, willlead to acceptably accurate results.

For example, in the coarse mesh (or the coarser mesh) of the componentmodel, the average volume or the average edge length of the finiteelements, used for the mesh, in at least one area of the component modelor in the whole component model, is larger than in the fine mesh.

The automatic description of the component model by a fine and/or coarseor coarser mesh is known, for example, from the standard software ABAQUSand, thus, can be executed. This also applies to the determination of anatural frequency or a natural oscillation mode of the naturaloscillation, based on a mesh that has been automatically generatedbeforehand.

The determination of the deformation of finite elements is known, forexample, from the standard software ABAQUS. For example, a finiteelement is more highly deformed than another, i) if the distancesbetween the nodes, which belong to this finite element, change morereadily, based on the calculation, than the distances between otherfinite elements, or ii) if the difference between the maximum volume andthe minimum volume during the period of the longest natural oscillationis greater than the corresponding difference of the other finiteelement.

As an alternative or in addition to the deformation of the finiteelements, a size that correlates to the deformation can also be used asa criterion for the next phase of coarsening the mesh. For example,based on the natural oscillation behavior, at least one area of thecomponent model can be determined and can be described by a coarsermesh, in that its associated finite elements are assigned, in particularby computation, less elongation, less stress, a smaller elongationgradient, a smaller stress gradient, a smaller edge length change, asmaller node displacement or a smaller volume change than the finiteelements in another area.

In a preferred further embodiment of the invention, based on the finemesh, at least one fine natural oscillation of the component model (thatis, a specific, fine mesh-based natural oscillation of the componentmodel) is determined automatically: in particular, a fine naturalfrequency (the fine mesh-based natural frequency of the component modelof a specific natural oscillation) and/or a fine natural oscillationmode (the fine mesh-based natural oscillation mode of the componentmodel of a specific natural oscillation) is determined. Then thecomponent model is described automatically, at least area by area, bymeans of a coarse mesh of finite elements, and based on the coarse mesh,at least one coarse natural oscillation of the component (a specific,coarse mesh-based natural oscillation of the component model) isdetermined: in particular, a coarse natural frequency (the coarsemesh-based natural frequency of the component model of a specificnatural oscillation) and/or a coarse natural oscillation mode (thecoarse mesh-based natural oscillation mode of the component model of aspecific natural oscillation), of the component model is determined.

Thereafter, the deviation of the coarse natural frequency from the finenatural frequency and/or the deviation of the coarse natural oscillationmode from the fine natural oscillation mode is (are) used, in particularautomatically, as a measure for the quality of conformance, quality oradaptiveness of the coarse mesh and, for example, displayed.

Therefore, according to the invention, the component model 101 isinitially described suitably, but memory-intensively by the fine mesh102, and, in so doing, the fine natural frequency (which is basedthereon) is accurately determined. Then the component model isdescribed, at least area by area, by a coarse mesh 103 with a low memoryspace requirement, so that the coarse natural frequency, which is basedthereon, is accurately determined. Whether this coarse mesh stilldescribes the component model in a suitable manner can then bedetermined based on the deviation of the coarse natural frequency fromthe fine natural frequency. The smaller the deviation, the more adaptiveor realistic is the description of the component model, based on thecoarse mesh.

Within the scope of the invention it is also clear that a plurality ofnatural oscillations, in particular natural frequencies, can bedetermined on the basis of the different meshes, and that thecorresponding deviations can be used as a criterion for quality ofconformance.

In an especially preferred embodiment of the invention, proceeding onthe basis of a fine mesh, the component model is describedautomatically, step by step, area by area, by increasingly coarsermeshes, especially until the deviation of the coarse natural frequencyfrom the fine natural frequency exceeds a predetermined or user-setthreshold value.

Then the deviation of the coarse natural frequency from the fine naturalfrequency can be used, in particular automatically, as the criterion foran abortive end of an automated mesh of a component model. Thus,proceeding on the basis of a fine mesh, the component model is describedautomatically step by step by an increasingly coarser mesh in at leastcertain areas.

Then (preferably, in addition) based on the fine mesh, the naturaloscillation behavior of the component model is determined, in apredetermined frequency range. Based on the natural oscillationbehavior, at least one area of the component model is determined, thefinite elements of which are more severely deformed than the finiteelements of another area of the component model, and the area of thecomponent model thus determined is described by an even finer mesh offinite elements or an even finer mesh with finite elements.

The natural oscillation behavior of the component model is basedpreferably on an overlapping of several (that is, from two up to all)natural oscillations that lie in a predetermined frequency range. Hence,in particular the deformation behavior of the finite elements isconsidered for the case that the component model oscillates with anoverlapping of several or all natural oscillations that lie in apredetermined frequency range.

The scope of the invention also includes a system for automaticallygenerating a mesh of a component model with a computer that is set up insuch a manner that a described method is carried out.

The scope of the invention also includes a computer program product forautomatically generating a mesh of a component model. Said computerprogram product comprises a computer readable storage medium, on which aprogram is stored that enables a data processing system to carry out adescribed method after said program has been loaded into a memory of adata processing system.

The invention is described in detail below with reference to oneexample.

The invention proposes a new method that is suitable, for example, foracoustics calculation. The acoustics calculation requires FE models thatreadily map the natural oscillation behavior of the modeled component.This mapping is intended to be achieved with the maximum number ofelement sizes. The drawback of small element sizes is the plurality ofelements and the related high memory space requirement of the models aswell as the long computing times. For the acoustics calculation theusual approach is to construct complete motor-transmission groups thatconsist of a very large number of components.

The proposed method takes as a basis a fine FE network (fine mesh). Thismethod is used to map the natural oscillation behavior as well aspossible. The FE network serves as the basis and reference foradditional calculations. For this model (described by the fine mesh),the natural oscillation behavior is calculated in a predeterminedfrequency range.

Each oscillation mode that occurs in this area generates a cyclicallyvariable deformation in the FE model (=FE network). As a result, certainareas exhibit high elongation, other areas exhibit only low elongation.In the areas with the high elongation it is important to map thestiffness correctly using fine FE elements (small element sizes, finemesh).

The areas of low elongation can, on the other hand, be modeled in acoarser manner. If the model is supposed to deliver good results for afrequency range, then the deformation of all modes that occur in thatfrequency range can be overlapped. The method, which is described below,is applied to the model with the corresponding total deformation.

The proposed method is intended to adapt the FE element size to theelongation. In this case the principle is to retain (or even to refine)a fine network in areas of high elongation, and to coarsen the FEnetwork (mesh) in areas of low elongation. The formulaic relationshipbetween the elongation and the FE element size can be selected by theuser in a manner which is known to those skilled in the art.

According to the invention, a new calculation is performed with thenetwork that has been modified in this way, and the results are comparedwith the preceding calculation with respect to the natural frequency andthe natural mode (for example, tested on excursions of selected points).If the deviation of the coarsened network is below a limit to bespecified, then the coarsening operation continues, according to theaforementioned method; otherwise the method is aborted, and the lastvalid calculation is used.

The foregoing disclosure has been set forth merely to illustrate theinvention and is not intended to be limiting. Since modifications of thedisclosed embodiments incorporating the spirit and substance of theinvention may occur to persons skilled in the art, the invention shouldbe construed to include everything within the scope of the appendedclaims and equivalents thereof.

What is claimed is:
 1. A method for simulating a physical property of acomponent model comprising a computer accessible construction model of atechnical structure, by automatically generating a mesh of the componentmodel, said method comprising: initially describing, by using aprocessor, the component model by means of a fine mesh of finiteelements; based on the fine mesh, determining, by using the processor, anatural oscillation behavior of the component model; based on thenatural oscillation behavior, identifying, by using the processor, atleast one area of the component model whose finite elements are lessdeformed than the finite elements of another area of the componentmodel; and modifying, by using the processor, the description of theidentified area of the component model by means of a coarser mesh offinite elements, wherein an average volume of finite elements of thecoarser mesh is larger than an average volume of finite elements of thefine mesh, or an average edge length of finite elements of the coarsermesh is larger than an average edge length of finite elements of thefine mesh.
 2. The method as claimed in claim 1, wherein: based on thefine mesh, at least one fine natural oscillation of the component modelis determined; the component model is further described by means of acoarse mesh of finite elements; based on the coarse mesh, at least onecoarse natural oscillation of the component model is determined; and adeviation of the coarse natural oscillation from the fine naturaloscillation is used as a measure for the quality of the coarse mesh. 3.The method as claimed in claim 1, wherein, proceeding from the finemesh, the component model is described step by step by increasinglycoarser meshes, until a deviation of a coarse natural oscillation from afine natural oscillation exceeds a threshold value.
 4. The method asclaimed in claim 1, wherein: based on the natural oscillation behavior,at least one other area of the component model, the finite elements ofwhich are deformed to a greater degree than the finite elements of yetanother area of the component model, is identified; and the otheridentified area is described by a finer mesh of finite elements.
 5. Themethod as claimed in claim 1, wherein the natural oscillation behavioris based on an overlapping of several natural oscillations that lie in apredetermined frequency range.
 6. A system for simulating a physicalproperty of a component model comprising a computer accessibleconstruction model of a technical structure, by automatically generatinga mesh of the component model, said system comprising a computer that isset up in such a manner that: the component model is initially describedby means of a fine mesh of finite elements; based on the fine mesh, anatural oscillation behavior of the component model is determined; basedon the natural oscillation behavior, at least one area of the componentmodel is identified whose finite elements are less deformed than thefinite elements of another area of the component model; and thedescription of the identified area of the component model is modified bymeans a coarser mesh of finite elements, wherein an average volume offinite elements of the coarser mesh is larger than an average volume offinite elements of the fine mesh, or an average edge length of finiteelements of the coarser mesh is larger than an average edge length offinite elements of the fine mesh.
 7. Computer program product forsimulating a physical property of a component model comprising acomputer accessible construction model of a technical structure, byautomatically generating a mesh of the component model, said computerprogram product comprises a non-transitory computer readable storagemedium, on which a program is stored that enables a data processingsystem, after said program has been loaded into a memory of a dataprocessing system, such that: the component model is initially describedby means of a fine mesh of finite elements; based on the fine mesh, thenatural oscillation behavior of the component model is determined; basedon the natural oscillation behavior, at least one area of the componentmodel is identified whose finite elements are less deformed than thefinite elements of another area of the component model; and thedescription of the identified area of the component model is modified bymeans of a coarser mesh of finite elements, wherein an average volume offinite elements of the coarser mesh is larger than an average volume offinite elements of the fine mesh, or an average edge length of finiteelements of the coarser mesh is larger than an average edge length offinite elements of the fine mesh.